Polynomial mixing for white-forced Kuramoto-Sivashinsky equation on the whole line
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917839227584512 |
|---|---|
| author | Gao, Peng |
| author_facet | Gao, Peng |
| contents | Our goal in this paper is to investigate ergodicity of white-forced Kuramoto-Sivashinsky equation (KSE) on the whole line. Under the assumption that sufficiently many directions of the phase space are stochastically forced, we can prove that the dynamics is attractive toward a unique invariant probability measure with polynomial rate of any power. In order to prove this, we further develop coupling method and establish a sufficiently general criterion for polynomial mixing. The proof of polynomial mixing for KSE is obtained by the combination of the coupling criterion and the Foiaş-Prodi estimate of KSE on the whole line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial mixing for white-forced Kuramoto-Sivashinsky equation on the whole line Gao, Peng Dynamical Systems Analysis of PDEs Probability Our goal in this paper is to investigate ergodicity of white-forced Kuramoto-Sivashinsky equation (KSE) on the whole line. Under the assumption that sufficiently many directions of the phase space are stochastically forced, we can prove that the dynamics is attractive toward a unique invariant probability measure with polynomial rate of any power. In order to prove this, we further develop coupling method and establish a sufficiently general criterion for polynomial mixing. The proof of polynomial mixing for KSE is obtained by the combination of the coupling criterion and the Foiaş-Prodi estimate of KSE on the whole line. |
| title | Polynomial mixing for white-forced Kuramoto-Sivashinsky equation on the whole line |
| topic | Dynamical Systems Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2408.00592 |